Juan:

I am not sure how to respond - except to say that I do not know if Derrida has appropriated the figure of "scene" from Lacan or Freud.  But in terms of the elliptical relationship of this figure to his many writings, I think we might have to think of "scene" in relation to the performativity of "texts,"  which are also always repetitions of a kind: so - yes - theatricallly, the "scene" is written to be re-played, over and over again.  The "scene" is also a space - as opening, as interval.  I look at the "scene of writing" as space where one can momentarily engage with and reflect on what writing might be - as Derrida enjoins in his essay, "Freud and the Scene of Writing," the question is not what is the psyche that writing can serve as an analogy for it, but rather, what is writing that it can be represented by the psyche!  and so, "text," and spectrality, inheritance, hospitality . . . .
The questions you are asking are insightful, and I think you are already coming to a place of playing with the figure of scene:  but no definitive or essential statements about "scene" in Derrida are possible, because of the force of differance, of resistance and reception, of displacement and deferral, - "No Weg without Umweg"!! 
I hope I haven't thrown more mud on the question.
best,
Karen